Consider the null hypothesis that the population mean is 100 and the alternative hypothesis that it is not equal to 100 . A 99% confidence interval for the mean is [97,104], while a 95% confidence interval for the mean is [99,101]. Which of the following is true? The null hypothesis is rejected at 5% significance, but not at 1%. The null hypothesis is rejected at 1% significance, but not at 5%. The null hypothesis is rejected at both 1% and 5% significance. The null is not rejected at either 1% nor 5% significance. Consider this correlogram from a regression analysis with three regressors. Which of the following is the correct assessment regarding multicollinearity in the model? The model has a problem due to the high degree of correlation between x2 and x3. The model has no problem with multicollinearity because none of the pairs are perfectly multicollinear. The model has a problem with perfect multicollinearity evidenced by the 1 's on the diagonal. The model has a problem with multicollinearity due to the low correlation between x1 and 2. X is a random variable from a population we can consider infinite which follows an exponential distribution with mean of 2 and variance of 4 . If repeated random samples of X are taken of size 50 , and for each the sample average is calculated, what is the distribution of the sample average? Approximately normal with mean 2 and variance 0.08 Approximately exponential with mean 2 and variance 0.08 Binomial with mean np and variance npq. Approximately normal with mean 0.04 and variance 0.28 . Page 2 of 25 New York City has 5,225,185 registered voters. Quinnipiac University polled 1310 New York City registered vote 37% of the voters surveyed responded that they approved of the mayor's job performance. What is the 90% confidence interval for the proportion of New York City registered voters who approve of the mayor's job performance